Solve 3/7div1/3+5/7div3/10

$$\frac { 3 } { 7 } \div \frac { 1 } { 3 } + \frac { 5 } { 7 } \div \frac { 3 } { 10 }$$

Evaluate

$$\frac{11}{3}\approx 3.666666667$$

Solution Steps

Divide \frac{3}{7} by \frac{1}{3} by multiplying \frac{3}{7} by the reciprocal of \frac{1}{3}.

$$\frac{3}{7}\times 3+\frac{\frac{5}{7}}{\frac{3}{10}}$$

Express \frac{3}{7}\times 3 as a single fraction.

$$\frac{3\times 3}{7}+\frac{\frac{5}{7}}{\frac{3}{10}}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{7}+\frac{\frac{5}{7}}{\frac{3}{10}}$$

Divide \frac{5}{7} by \frac{3}{10} by multiplying \frac{5}{7} by the reciprocal of \frac{3}{10}.

$$\frac{9}{7}+\frac{5}{7}\times \frac{10}{3}$$

Multiply \frac{5}{7} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{7}+\frac{5\times 10}{7\times 3}$$

Do the multiplications in the fraction \frac{5\times 10}{7\times 3}.

$$\frac{9}{7}+\frac{50}{21}$$

Least common multiple of 7 and 21 is 21. Convert \frac{9}{7} and \frac{50}{21} to fractions with denominator 21.

$$\frac{27}{21}+\frac{50}{21}$$

Since \frac{27}{21} and \frac{50}{21} have the same denominator, add them by adding their numerators.

$$\frac{27+50}{21}$$

Add 27 and 50 to get 77.

$$\frac{77}{21}$$

Reduce the fraction \frac{77}{21} to lowest terms by extracting and canceling out 7.

$$\frac{11}{3}$$

Factor

$$\frac{11}{3} = 3\frac{2}{3} = 3.6666666666666665$$